The IAU 2000 Resolutions for Astrometry, Celestial Mechanics, and Metrology in the Relativistic Framework: Explanatory Supplement

Söffel, M.; Klioner, Sergei A.; Petit, Gérard; Wolf, Peter; Kopeikin, Sergei M.; Bretagnon, P.; Brumberg, V. A.; Capitaine, N.; Damour, Thibault; Fukushima, Toshio; Guinot, B.; Huang, Tian-Yi; Lindegren, L.; Ma, C.; Nordtvedt, Kenneth; Ries, John; Seidelmann, P. K.; Vokrouhlický, David; Will, Clifford M.; Chun, Xu

doi:10.1086/378162

Cited by 343 publications

(603 citation statements)

References 32 publications

(49 reference statements)

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“…The law of transformation between the local harmonic coordinates extends the linear Lorentz transformation to the class of harmonic polynomials that are solutions of the homogeneous wave equation [53][54][55][56][57][58]. They have a great practical value for modern fundamental astronomy [59,60]. The second important observation is that the class of the harmonic coordinates is actually much more generic than physicists used to think.…”

Section: A the Field Equationsmentioning

confidence: 99%

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Gravitational bending of light by planetary multipoles and its measurement with microarcsecond astronomical interferometers

2007

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General-relativistic deflection of light by mass, dipole, and quadrupole moments of the gravitational field of a moving massive planet in the solar system is derived in the approximation of the linearized Einstein equations. All terms of order 1 as are taken into account, parametrized, and classified in accordance with their physical origin. The monopolar light-ray deflection, modulated by the radial Doppler effect, is associated with the total mass and radial velocity of the gravitating body. It displaces the apparent positions of stars in the sky plane radially away from the origin of the celestial coordinates associated with the planet. The dipolar deflection of light is due to a translational mismatch of the center of mass of the planet and the origin of the planetary coordinates caused by the inaccuracy of planetary ephemeris. It can also originate from the difference between the null cone for light and that for gravity that is not allowed in general relativity but can exist in some of the alternative theories of gravity. The dipolar gravity field pulls the apparent position of a star in the plane of the sky in both radial and orthoradial directions with respect to the origin of the coordinates. The quadrupolar deflection of light is caused by the physical oblateness, J 2 , of the planet, but in any practical experiment it will have an admixture of the translation-dependent quadrupole due to inaccuracy of planetary ephemeris. This leads to a bias in the estimated value of J 2 that should be minimized by applying an iterative data reduction method designed to disentangle the different multipole moments and to fit out the translation-dependent dipolar and quadrupolar components of light deflection. The method of microarcsecond interferometric astrometry has the potential of greatly improving the planetary ephemerides, getting unbiased measurements of planetary quadrupoles, and of thoroughly testing the null-cone structure of the gravitational field and the speed of its propagation in the near-zone of the solar system. We calculate the instantaneous patterns of the light-ray deflections caused by the monopole, the dipole, and the quadrupole moments, and derive equations describing apparent motion of the deflected position of the star in the sky plane as the impact parameter of the light ray with respect to the planet changes due to its orbital motion. We discuss the observational capabilities of the near-future optical (SIM) and radio (SKA) interferometers for detecting the Doppler modulation of the radial deflection, and the dipolar and quadrupolar light-ray bendings by Jupiter and Saturn.

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Section: A the Field Equationsmentioning

confidence: 99%

“…8. As the planet moves from ' ÿ =2 to ' =2 along the Y axis, the deflected position of the star describes the curve x 02 y 02 ÿ px 0 2 p 2 x 02 y 02 ; (59) shown in the middle graph of Fig. 9.…”

Section: Dynamic Patternsmentioning

confidence: 99%

Gravitational bending of light by planetary multipoles and its measurement with microarcsecond astronomical interferometers

2007

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“…A theory of relativistic reference system has been formulated by Damour et al (1991, DSX-I), improving and extending earlier work by Brumberg & Kopeikin (BK;1989a,b). A standard reference is Soffel et al (2003). For the VLBI model this theory provides precise definitions of the BCRS and the GCRS and the relations between them.…”

Section: Resultsmentioning

confidence: 99%

Advanced relativistic VLBI model for geodesy

Söffel

Kopeikin

Han

2016

J Geod

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Abstract:Our present relativistic part of the geodetic VLBI model for Earthbound antennas is a consensus model which is considered as a standard for processing high-precision VLBI observations. It was created as a compromise between a variety of relativistic VLBI models proposed by different authors as documented in the IERS Conventions 2010. The accuracy of the consensus model is in the picosecond range for the group delay but this is not sufficient for current geodetic pur-poses. This paper provides a fully documented derivation of a new relativistic model having an accuracy substantially higher than one picosecond and based upon a well accepted formalism of relativistic celestial mechanics, astrometry and geodesy. Our new model fully confirms the consensus model at the picosecond level and in several respects goes to a great extent beyond it. More specifically, terms related to the acceleration of the geocenter are considered and kept in the model, the gravitational time-delay due to a massive body (planet, Sun, etc.) with arbitrary mass and spin-multipole moments is derived taking into account the motion of the body, and a new formalism for the time-delay problem of radio sources located at finite distance from VLBI stations is presented. Thus, the paper presents a substantially elaborated theoretical justification of the consensus model and its significant extension that allows researchers to make concrete estimates of the magnitude of residual terms of this model for any conceivable configuration of the source of light, massive bodies, and VLBI stations. The largest terms in the relativistic time delay which can affect the current VLBI observations are from the quadrupole and the angular momentum of the gravitating bodies that are known from the literature. These terms should be included in the new geodetic VLBI model for improving its consistency.

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“…Both source parameters and x obs are defined in the underlying relativistic reference system called Barycentric Celestial Reference System (BCRS) and described e.g. in [43]. The correction δu is perpendicular to u (δu · u = 0) and represent the perturbation of the direction towards the source as observed by a fictitious observer that is at rest with respect to the BCRS and co-located with the real (moving) observer.…”

Section: The Deflection Formula From a Plane Gravitational Wavementioning

confidence: 99%

Gaia-like astrometry and gravitational waves

Klioner

2018

Class. Quantum Grav.

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This paper discusses the effects of gravitational waves on high-accuracy astrometric observations such as those delivered by Gaia. Depending on the frequency of gravitational waves, two regimes for the influence of gravitational waves on astrometric data are identified: the regime when the effects of gravitational waves directly influence the derived proper motions of astrometric sources and the regime when those effects mostly appear in the residuals of the standard astrometric solution. The paper is focused on the second regime while the known results for the first regime are briefly summarized.The deflection of light due to a plane gravitational wave is then discussed. Starting from a model for the deflection we derive the corresponding partial derivatives and summarize some ideas for the search strategy of such signals in high-accuracy astrometric data. In order to reduce the dimensionality of the parameter space the use of vector spherical harmonics is suggested and explained. The explicit formulas for the VSH expansion of the astrometric signal of a plain gravitational wave are derived.Finally, potential sensitivity of Gaia astrometric data is discussed. Potential astrophysical sources of gravitational waves that can be interesting for astrometric detection are identified.PACS numbers: 95.10. Jk, 95.55.Br, 95.75.Pq, 95.85.Sz, 04.80.Nn

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The IAU 2000 Resolutions for Astrometry, Celestial Mechanics, and Metrology in the Relativistic Framework: Explanatory Supplement

Cited by 343 publications

References 32 publications

Gravitational bending of light by planetary multipoles and its measurement with microarcsecond astronomical interferometers

Gravitational bending of light by planetary multipoles and its measurement with microarcsecond astronomical interferometers

Advanced relativistic VLBI model for geodesy

Gaia-like astrometry and gravitational waves

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